Olivier Lhomme

Local search with constraint propagation and conflict-based heuristics

Search algorithms for solving CSP (Constraint Satisfaction Problems) usually fall into one of two main families: local search algorithms and systematic algorithms. Both families have their advantages. Designing hybrid approaches seems promising since those advantages may be combined into a single approach. In this paper, we present a new hybrid technique. It performs a local search over partial assignments instead of complete assignments, and uses filtering techniques and conflict-based techniques to efficiently guide the search. This new technique benefits from both classical approaches: a priori pruning of the search space from filtering-based search and possible repair of early mistakes from local search. We focus on a specific version of this technique: tabu decision-repair. Experiments done on open-shop scheduling problems show that our approach competes well with the best highly specialized algorithms.

Arc-Consistency Filtering Algorithms for Logical Combinations of Constraints

The logical connectives between constraints, sometimes called meta-constraints, although extremely useful for modelling problems, have either poor filtering algorithms or are not very efficient. We propose in this paper new filtering algorithms that achieve arc-consistency over those logical connectives. The principle is to export supports from a constraint.

Accelerating filtering techniques for numeric CSPs

Search algorithms for solving Numeric CSPs (Constraint Satisfaction Problems) make an extensive use of filtering techniques. In this paper we show how those filtering techniques can be accelerated by discovering and exploiting some regularities during the filtering process. Two kinds of regularities are discussed, cyclic phenomena in the propagation queue and numeric regularities of the domains of the variables. We also present in this paper an attempt to unify numeric CSPs solving methods from two distinct communities, that of CSP in artificial intelligence, and that of interval analysis.

An efficient filtering algorithm for disjunction of constraints

Disjunctions of constraints frequently appear in applications of constraint programming. In this paper, we propose a new filtering algorithm for the disjunctions of constraints. It performs the same domain reductions as constructive disjunction [1,2], but is more efficient.

Amortized Random Backtracking

Some nonsystematic search algorithms can deal with partial assignments of variables, and then can use constraint propagation techniques. Let us call them NSPA algorithms (Nonsystematic Search with Partial Assignments). For satisfiability or optimization problems, such NSPA algorithms scale a lot better than systematic algorithms. We show in this paper that naive NSPA algorithms have to pay a severe overhead due to the way they visit partial assignments. Amortizing the visits of partial assignments is an important feature which we introduce and analyze in this paper. We also propose a new NSPA algorithm that is amortized: it is called Amortized Random Backtracking, and performs a probabilistic exploration of the search space. It can be seen as an amortized version of iterative sampling and has given very good experimental results on a real life time tabling problem.